with \(Q_K\)  being the electric charge of the outgoing \(K\)  meson and \(\tau \)  being the isospin factor of the Kroll-Ruderman term. \(f_t\)  is the phenomenological form factor attaching to the amplitude of the \(t\) -channel \(K\)  exchange, which is given by Eq. (REF ). The auxiliary current \(C^\mu \)  for the \(\gamma p \rightarrow K^+\Lambda (1690)\)  reaction is chosen to be [1]}, [2]}, [3]}
\(C^\mu = - Q_K \tau \frac{f_t-\hat{F}}{t-q^2} (2q-k)^\mu - \tau Q_N \frac{f_s-\hat{F}}{s-p^2} (2p+k)^\mu , \) 
